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Determine nodal displacements using Galerkin’s method

1. Consider a two-dimensional problem governed by the differential equation
(this is Laplace’s equation) in a specified two-dimensional domain with
specified boundary conditions. How would you apply the Galerkin finite
element method?
Ref: Fundamentals of Finite Element Analysis, David V. Hutton, 2004.
2. For the bar subjected to the uniform line load in the axial direction shown in
the figure, determine the nodal displacements using Galerkin’s method with
two equal-length elements. Let A =2in2 and E= 30*106 psi. Choose a
quadratic polynomial in the method. Compare this
weighted residual solution to the exact solution

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